Question

一个公平骰子的面为 $1, 1, 2, 2, 3, 3$ ，另一个公平骰子的面为 $4, 4, 5, 5, 6, 6$ 。掷这两个骰子并把朝上的数相加。和为奇数的概率是多少？

One fair die has faces $1, 1, 2, 2, 3, 3$ and another has faces $4, 4, 5, 5, 6, 6.$ The dice are rolled and the numbers on the top faces are added. What is the probability that the sum will be odd?

$\dfrac13$

$\dfrac49$

$\dfrac12$

$\dfrac59$

$\dfrac23$

答案：D

知识点：骰子（概率）奇偶性独立事件

难度评级：1240

解答：

第一个骰子为奇数（ $1$ 或 $3$ ）的概率为 $\dfrac23$ ，为偶数的概率为 $\dfrac13$ 。第二个骰子为奇数（ $5$ ）的概率为 $\dfrac13$ ，为偶数的概率为 $\dfrac23$ 。

两个数奇偶性不同时和为奇数，所以概率为 $\dfrac13 \cdot \dfrac13 + \dfrac23 \cdot \dfrac23 = \dfrac19 + \dfrac49 = \dfrac59.$

所以正确答案是 D。

The first die is odd (a $1$ or $3$ ) with probability $\dfrac23$ and even with probability $\dfrac13.$ The second die is odd (a $5$ ) with probability $\dfrac13$ and even with probability $\dfrac23.$

The sum is odd when the two parities differ: $\dfrac13 \cdot \dfrac13 + \dfrac23 \cdot \dfrac23 = \dfrac19 + \dfrac49 = \dfrac59.$

Thus, D is the correct answer.

2005 AMC 10B 第 9 题

答案：D

难度评级：1240

解答：

其他年份的第 9 题